What are the differences between a knowledge base and a knowledge graph?
Based on the related Wikipedia, a knowledge base (KB) is:


  a technology used to store complex structured and unstructured information used by a computer system. The initial use of the term was in connection with expert systems which were the first knowledge-based systems.


As there are different representation model for a KB, we can find different terminology in different domains. For example, in some AI articles, it's called ontology.

Knowledeg graph (KG) is another object model to KB realization which is introduced by Google for its search engine (as you have mentioned). Hence, KG is a specification of KB. You can find more information in the paper Knowledge Graphs, such as more history about the KG or a formal definition of that: 


  knowledge graph is a graph of data intended to accumulate and convey knowledge of the real world, whose nodes represent entities of interest and whose edges represent relations between these entities.


Moreover, you can find some articles about contextual KG (CKG) in the paper Learning Contextual Embeddings for Knowledge Graph Completion and KG$^2$: Learning to Reason Science Exam Questions with Contextual Knowledge Graph Embeddings.